Yes, Material Design was developed and is used by Google.
Material Design isn't really a framework as much as it is a set of very strict design guidelines which in turn is used by independent developers to create libraries for you to use in your own projects. You can look at Material UI which was developed by Call-em-all to be a Material Design library for React. Then there's Angular Material which was developed by Google's Angular team. There's also many other pure css implementations you can use - see Material Design Lite and Materialize. If you're brave you can even develop your own library that use the Material Design guidelines.

Bootstrap was developed by Twitter many years ago and is a full blown UI framework. Many people have made their own customised versions of Bootstrap as well. There's even a few Bootstrap based libraries that use Material Design - see Material Design for Bootstrap 4.

I should have probably been a bit clearer when I suggested you don't use Bootstrap. I should have probably said don't use Bootstrap as-is. Either use a customised version or customise it yourself so that at least your app doesn't look like all the other apps out there - and essentially gets lost in the masses. If you do that then Bootstrap can still be a very good choice.